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A garden hose on the ground, water with enough speed flows out at its end. In the beginning, the hose is bent. Assuming only the force caused by bending and the friction force on the ground act on the hose, will the hose eventually become a straight hose?

Assume that the hose is very soft.

enter image description here

picture source

Does the hydrodynamic force caused by the bending of the hose finally make the hose a straight line? If the answer to this question is yes, then the movement of the hose end is not the result of hose bending.

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As the water flows through the hose, its course change and moves to the right. This redirection of the flow is caused by a force to the right applied by the left inside wall of the hose.

Newton's Third Law (for every force there is an equal and opposite force) means that there must be a corresponding force applied by the water to the hose, pushing it to the left. That force is what the brown arrows represent.

So, there is one force trying to move the bent part of the hose to the left, and there is the force of friction between the hose and the ground trying to keep the hose in place.

If the first force is greater than the other, the hose will move, causing the lower part of the bend to straighten and the upper part of the bend to move farther up the length of the hose; otherwise it will remain at rest.

Update: note that this answer is for the original question only. The question of what happens at the far end of the hose was added later, and really should be a completely different question.

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  • $\begingroup$ Because of the damped motion, the hose tends to be straight, assuming that the friction on the ground is relatively small. Right? $\endgroup$
    – enbin
    Commented Oct 1, 2020 at 13:59
  • $\begingroup$ What about straightening the very last piece? $\endgroup$ Commented Oct 2, 2020 at 17:49
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In the case of an ideally flexible hose (and without friction with the ground, say in empty space), the hose will never be bent exactly straight, as the force of the water hits the inner hose increasingly tangent. it will take an infinite time to do so.

If the hose lays on the ground, a minimum speed of the water is required to make the hose move. If the water runs through the hose, it will depend on how much force the curved hose gives against the force of the water. You can imagine that if the water is running slow, not much happens to the hose.
If the water is given more speed, the force on the inner hose will rise. And thus the oppositely directed friction force.
When you give enough speed to the water this friction force will be overcome and the hose starts to move. In the picture to the left. As I said in the first paragraph, the hose can never be straightened out exactly (you need an infinite speed of the water, or better, a speed close to the speed of light). During this process of moving there will be some straightening.
If the speed of the water is increased more the hose will move faster. But the hose will not straighten out. Instead, it will start to behave chaotically. Try it in the garden or where ever.
So, if the speed of the water gets too high, the hose will end up in a chaotic motion and not get straight.

I agree also though with what is written in the first answer:

If the first force is greater than the other, the hose will move, causing the lower part of the bend to straighten and the upper part of the bend to move farther up the length of the hose; otherwise it will remain at rest.

But before the end is reached the hose will start to behave in an unpredictable way (see the first link below).

I made the assumption the beginning of the bending of the hose stays where it is, which isn't the case. You can clearly see this phenomenon in those high, thin plastic cylinder, through which air is blown:

enter image description here

See also this and this video. Or this one.

Though the question is, can the last piece be put straight because the force of the speeding water will approach a parallel direction to the hose, so the normal force on the hose approaches zero. In the real world, of course, the hose is straightened out.
If the hose is placed with its straight piece on a wall, the force of the water will, in the ideal case (you can think for yourself what that means), will not be able to totally complete the straightening. It's that last piece...

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – tpg2114
    Commented Oct 3, 2020 at 13:39

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